Cosmic Distance Ladder Spiral/Elliptical Galaxy Kinematics
Beena Meena Astro 8400 Cosmic Distance Ladder
15 Mpc to 200 Mpc
Upto 15 Mpc
Spirals
“The Essential Cosmic Perspective”, Bennett et al Elliptical: Faber-Jackson Relation
4/20/20 Beena Meena - Astro 8400 2 Galaxy Rotation: Basics
Km/sec
https://pages.uoregon.edu/jimbrau/BrauImNew/Chap24/6th/24_11Figure-F. jpg
4/20/20 Beena Meena - Astro 8400 3 Galaxy Rotation from HI (λ 21cm) line Credit: JRob’s prospectus Note: Line width needs to be corrected for inclination: Width/sin(i)
4/20/20 Beena Meena - Astro 8400 4 The Tully - Fisher Relation
“A new method of determining distance to galaxies”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 Line width∝ Absolute Magnitude (Brighter galaxies rotate faster)
4/20/20 Beena Meena - Astro 8400 5 Original Tully Fisher Relation (TFR) “A new method of determining distance to galaxies”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 • Photometric measurements (M81 & M101) : Cepheid distances
• Note: Absolute Magnitude M∝ d
• Radio observation: 91 m NRAO
• Apparent Mag. (m): Optical (B)
• Find Best fit: Calibration
• Apply to distant galaxies
4/20/20 Beena Meena - Astro 8400 6 TFR for distance measurement
1) Distance Modulus µ = m – M Luminosity
ΔV(0): H1 line width corrected for inclination mpg : Photographic magnitude
Slope (⍺) Log(L) 2) Hubble Constant H0 = V/d Preliminary Value = 80 km s−1 Mpc−1
ΔV(0) 4/20/20 Beena Meena - Astro 8400 7 Progress: TF Relationship
• Moved on from visible to other bandpasses
• Tully Fisher Relation is tighter in I band
−1 −1 • H0 = 71 +/-7 km s Mpc
Sakai et al., ApJ 529, 698 (2000)
4/20/20 Beena Meena - Astro 8400 8 Advanced TF Relation (by Tully) Tully et al. , AJ , 2013, 146, 4
Cosmicflows2 • Cosmicflows3: 17,669 entries
• Photometry at 3.6 µm Observation: Spitzer Space Telescope
• Cepheid, Tip of the Red Giant Branch (TRGB), Type Ia supernova (SNIa): Distance Calibrations
−1 −1 • H0 = 76.2 +/-2.7 km s Mpc
4/20/20 Beena Meena - Astro 8400 9 More recent Results: • Lelli Federco et al., MNRAS,2019 484,3 • A const. M/L ratio breaks at Low Luminosity galaxies • Include gas mass so total mass = Stellar mass + gas (Baryonic mass) • Baryonic Tully –Fischer relation (from McGaugh et. al. 2000, 533,2 ) • Slope (⍺) = 3.85 ± 0.09
Sheii, J. R. et al., AAS 2020, 4,4 “Tully Fischer for southern galaxies with HIPASS and WISE” −1 −1 Hubble Const. H0 = 73.3 ± 1 km s Mpc
Range of Distance measurements: upto z = 1.4 Lorenzo et al., A&A,2010, 521,A27
4/20/20 Beena Meena - Astro 8400 10 Limitations & Source of Errors
• Does not consider mass from dark Matter: Halo(?)
• Constant M/L ratio for a range of luminosity
• Errors due to measurement of inclination (5% uncertainties in inclination amounts to 9% error in line width: cosmicflow2, Tully et al 2013)
• More: Uncertainties in measurement of apparent magnitude
4/20/20 Beena Meena - Astro 8400 11 Elliptical Galaxies
• Prolate (Rugby ball) shape
• Generally composed of older, low-mass stars
• Minimal star formation
• Hardly rotating: Can’t use Tully Fischer
• Stellar velocity dispersion M87: Wikipedia
4/20/20 Beena Meena - Astro 8400 12 Faber–Jackson relation
• Presented by astronomers Sandra M. “Velocity dispersions and mass-to-light ratios for elliptical galaxies”, Faber, S. M.; Jackson, R. E. Faber and Robert Earl Jackson in 1976 1976,ApJ, 204, 668
• Similar to TF L ∝ σˠ Velocity dispersion(σ) σ = Stellar velocity dispersion ˠ ∼ 4
4/20/20 Beena Meena - Astro 8400 13 Fundamental Plane (FP)
• To minimize the scatter in Faber Jackson
• Djorgovski, S.; Davis, Marc 1987 coined the term Fundamental Plane:
• (Lum)⍺(Radius)β(vel. dispersion)ˠ = Const.
• Any one of the three parameters may be Dn = Diameter measured at estimated from the other two. 20.75 mag per square arcsecond Dressler et al., 1987, ApJ 313, 42
4/20/20 Beena Meena - Astro 8400 14 (FP) (somewhat) Recent Results:
Ellipticals S0 Galaxies
Reduced Scattering from 25% (Dresseler et al. 1987) to 20% for each galaxy
Bernardi et al.,2002, AJ 123, 2159
4/20/20 Beena Meena - Astro 8400 15 Summary
• Distance Ladder Rung 5: Galaxy Kinematics Best within ≈ 200Mpc
• Spiral-> Tully Fisher : L ∝ (ΔV)⍺ ; ⍺ ∼ 3 to 4
• Elliptical -> Faber Jackson: L ∝ σˠ or Fundamental Plane
4/20/20 Beena Meena - Astro 8400 16 Thank you!
4/20/20 Beena Meena - Astro 8400 17